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Fishery Bulletin 102(4) 



GAM smoothers Before a GLM was constructed, a 

 GAM helped group continuous variables into catego- 

 ries. Fitting the GLM model with categorized variables 

 was necessary to extrapolate bycatch rates in order to 

 derive a total estimate of the bycatch of sea turtles in 

 scallop dredges in the controlled access areas. All of the 

 variables tested in the GLM model were first fitted to 

 a GAM, in which the parameters of the continuous pre- 

 diction variables were estimated by a smoothing spline. 

 Variable values were grouped according to whether they 

 had a positive or negative influence on the bycatch rate 

 (i.e., the group explained more or less of the bycatch 

 rate). 



Development of a GLM bycatch model Because bycatch 

 events were counts ranging from zero or one, a logistic 

 regression was used to model the probability of sea 

 turtle bycatch (GLM function, SPLUS 6.1, Seattle, WA). 

 Each dredge haul is a data point and the response was 

 whether turtle bycatch was zero or one. Probability of 

 sea turtle bycatch (p) was calculated as 



p = e y 1 1 + e y 



y = P +P 1 x 1 +P 2 x 2 +...+ p i x i , 



where p t is a parameter coefficient; 

 x l is a predictor variable; and 

 y is a sea turtle bycatch event. 



Dredge hauls are assumed to be independent because 

 turtles were never simultaneously caught in both dredges 

 operating from a vessel during a single haul. 



A forward stepwise selection method was used to de- 

 termine the best fitting model. Model parameters were 

 estimated by maximizing the log-likelihood function. 

 The null model was the first model in the stepwise 

 process and was specified with a single intercept term 

 as 



H : logiturtle bycatch) = 1. 



At each step, a new variable was added to the null model 

 (Appendix 1) and tested against the former model formu- 

 lation (ANOVA function, chi-square test) to determine 

 the better fitting model. A preliminary assessment of a 

 broad suite of gear characteristics and environmental 

 factors indicated that 10 variables could significantly 

 affect bycatch rates. The main effects of each variable 

 were tested in the stepwise selection process as well 

 as the interaction between season and temperature. 

 Because the order of the predictor variables affects their 

 significance, main effects were entered in various orders. 

 If a P-value was less than 0.05, then the additional vari- 

 able was considered to explain more of the variability in 

 bycatch than a model without that variable. Each new 

 model was also compared against the former model by 

 using the Akaike information criterion (AIC), which is 

 defined as 



A/C = -21og(L(0ly)) + 2.K', 



where log(L(6H y )) = the numerical value of the log-likeli- 

 hood at its maximum point; and 

 K = the number of estimable parameters 

 (Burnham and Anderson, 20021. 



The AIC is a measure of the level of parsimony, defined 

 as a model that fits the data well and includes as few 

 parameters as necessary (Palka and Rossman, 2001). If 

 the AIC value decreases, the new combination of vari- 

 ables in the model fit the data better. 



To investigate whether the bycatch data are over- 

 dispersed, that is. where the sampling variance exceeds 

 the theoretical variance, the GLM model was refitted 

 by using a quasi-likelihood function. When data are 

 over-dispersed, the estimated over-dispersion parameter 

 is generally between 1 and 4 (Burnham and Ander- 

 son, 2002). The over-dispersion parameter fitted to the 

 global model was 0.61, indicating these data were not 

 over-dispersed and error assumptions of the binomial 

 model were appropriate for analyzing these data. 



Alias patterns in the final model were examined to 

 assess correlation among the explanatory variables. 

 The fit of the final model was assessed by plotting the 

 observed turtle bycatch against the predicted turtle 

 bycatch. The r 2 value indicated how well predictions 

 from the linear model fit the actual data. 



Bycatch rate estimates The spatial and temporal strati- 

 fication of bycatch rates in each of the controlled access 

 areas was determined by the explanatory variables in 

 the best-fitting GLM. Parameter estimates from the 

 model were used to predict the bycatch rate for each 

 stratum. 



The coefficient of variation (CV) for each bycatch 

 rate was estimated by bootstrap resampling (Efron and 

 Tibshirani, 199.3). The resampling unit was a scallop 

 dredge haul. Replicate bycatch rates were generated 

 with the best-fitting GLM model, by sampling with 

 replacement 1000 times from the original data set. 

 The CV was defined as the standard deviation of the 

 bootstrap replicate bycatch rates in a stratum divided 

 by the bycatch rate for that stratum estimated from the 

 original data. Variances and CVs of combined estimates 

 were based on means weighted by their respective vari- 

 ances (Wade and Angliss, 1997). 



Total bycatch The total estimated turtle bycatch in 

 each stratum was calculated as the product of predicted 

 bycatch per dredge haul (i.e., the predicted bycatch 

 rate) for that stratum and the total number of dredge 

 hauls accomplished by the commercial fishery in that 

 stratum: 



^ Predicted bycatch 

 V Dredge hauls t 



where ; = stratum 



 [Total dredge hauls),. 



